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  • Open Access

Asymptotic Padé predictions up to six loops in QCD and eight loops in λϕ4

J. A. Gracey, I. Jack*, and D. R. T. Jones

  • *Contact author: dij@liverpool.ac.uk
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Phys. Rev. D 113, 096013 – Published 18 May, 2026

DOI: https://doi.org/10.1103/vzzh-vbjb

Abstract

We assess the accuracy of our previous asymptotic Padé predictions of the five-loop QCD β-function and quark mass anomalous dimension in the light of subsequent exact results. We find the low-order coefficients in an expansion in powers of NF (the number of flavors) were correct to within 1%. Furthermore an examination of recent results in λϕ4 theory indicates that the asymptotic Padé methods deliver predictions which increase in accuracy with loop order. Encouraged by this, we present six-loop asymptotic Padé predictions for the QCD β-function and quark mass anomalous dimension and also for the eight-loop β-function in O(N) λϕ4 theory.

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Phys. Rev. D 113, 096013– Published 18 May, 2026
  • Received 21 January 2026
  • Accepted 6 April 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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